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Perturbation bounds and truncations for a class of Markovian queues

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Abstract

We consider time-inhomogeneous Markovian queueing models with batch arrivals and group services. We study the mathematical expectation of the respective queue-length process and obtain the bounds on the rate of convergence and error of truncation of the process. Specific queueing models are shown as examples.

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Acknowledgments

The authors are grateful to the referees and the Editors for helpful comments and suggestions. This work was supported by the Russian Foundation for Basic Research, Project Nos. 12-07-00109, 12-07-00115, 13-07-00223, 14-07-00041, 14-07-00082, 14-07-00090.

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Authors and Affiliations

  1. Vologda State University, Vologda, Russia

    Alexander Zeifman, Yacov Satin & Anna Korotysheva

  2. Institute of Informatics Problems, Russian Academy of Sciences, Moscow, Russia

    Alexander Zeifman, Victor Korolev & Vladimir Bening

  3. Institute of Socio-Economic Development of Territories, Russian Academy of Sciences, Vologda, Russia

    Alexander Zeifman

  4. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia

    Victor Korolev & Vladimir Bening

Authors
  1. Alexander Zeifman
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  2. Victor Korolev
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  3. Yacov Satin
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  4. Anna Korotysheva
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  5. Vladimir Bening
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Correspondence to Alexander Zeifman.

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Zeifman, A., Korolev, V., Satin, Y. et al. Perturbation bounds and truncations for a class of Markovian queues. Queueing Syst 76, 205–221 (2014). https://doi.org/10.1007/s11134-013-9388-0

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  • DOI: https://doi.org/10.1007/s11134-013-9388-0

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